You will get a federal income tax refund for the unemployment exclusion if all of the following are true.
If all four of those conditions are true, The IRS will recalculate your tax return and send you the refund. It might be a couple of months before you get it. For more information see the following IRS announcements and FAQ.
IRS to recalculate taxes on unemployment benefits; refunds to start in May
IRS begins correcting tax returns for unemployment compensation income exclusion
IRS continues unemployment compensation adjustments, prepares another 1.5 million refunds
2020 Unemployment Compensation Exclusion FAQs
Q. How do I know if I should be expecting additional refund based on the (up to) $10,200 unemployment exclusion?
A. Prepare a test return with $10,200 less income and compare the result to the original return. You can use this tool
https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1
If your tax liability was already zero (line 16 of form 1040), it's unlikely that you will be getting more. But, it's possible, particularly if you become eligible for more EIC.